EPISTEMOLOGY PLUS VALUES EQUALS CLASSROOM
IMAGE OF MATHEMATICS
Paul Ernest
University of Exeter, UK
p.ernest(at)ex.ac.uk
Introduction
What is the impact of values on the mathematics classroom? In this paper I advance the thesis
that an epistemology or philosophy of mathematics combined with a set of values provides
the basis for the classroom image of mathematics. The four key terms in this claim are:
1. the epistemology or philosophy of mathematics – whose it is and how it can be
characterised?
2. the set of values involved – what is it and whose is it?
3. the classroom image of mathematics – what is it, whose is it and how is it manifested?
4. the interaction of 1 and 2 and the resultant product 3 – how do these factors interact and
what mechanisms and further complexities are involved?
In the sections below I sketch answers to these questions, but first I need to offer some
caveats. Inevitably any simple equation like this is a simplification. Such a model serves to
highlight the import and impact of both values and epistemology on the mathematics
classroom. However, both theoretically and empirically, developing and applying such a
model reveals layer upon layer of additional complexities that are factored out by the
simplifications involved. I shall delineate two philosophies of mathematics and two sets of
values and explore their combined impact on the classroom, but needless to say there are
many more variations of personal epistemologies and sets of values than this simple
dichotomisation reveals.1 In addition, such interactions do not take place in isolation, but in
social contexts, and these add many further layers of complexity.
I believe that much of what I claim is also applicable to the sciences, especially the physical
sciences. There are differences between philosophies of science and philosophies of
mathematics, but there are also similarities, which suggest that the parallel arguments can be
made for science education. For example, I distinguish absolutist and fallibilist philosophies
of mathematics below, and this parallels the distinction between realism and instrumentalism
in the philosophy of science.2
Why do learner images of mathematics matter? Below I argue that they are a large component
of learner attitudes and beliefs about mathematics. These play an important role in problem
1
In Ernest (1991) I outline five ideologies of education identified in the British scene at the time, each with its
own variant sets of values, philosophies of mathematics, and perspectives on the teaching and learning of
mathematics, and even this more extended model is acknowledged to be a simplification.
2
By realism I mean the view that scientific theories and statements are truths about the universe, whereas
instrumentalism is the view that they are humanly constructed conceptual tools that are are useful instruments, to
be discarded when they have served their purpose.
2
solving and in learner participation in advanced mathematical studies and careers. So
indirectly developing a positive image of mathematics leads to learner advancement and to
the benefit of society. The same holds true for science and technology.
1. The Epistemology / Philosophy of Mathematics
Absolutist Philosophies of Mathematics
There is a range of perspectives in the philosophy of mathematics which can be termed
‘absolutist’. These view mathematics as an objective, absolute, certain and incorrigible body
of knowledge, which rests on the firm foundations of deductive logic. Among twentieth
century philosophies, Logicism, Formalism, and to some extent Intuitionism and Platonism,
may be said to be absolutist in this way (Ernest 1991).
However, absolutist philosophies of mathematics are not concerned to describe mathematics
or mathematical knowledge as they are practiced or applied in the world around us. They are
concerned with the epistemological project of providing rigorous systems to warrant
mathematical knowledge absolutely. This project was set in motion following the crisis in the
foundations of mathematics arising from the introduction of Cantor’s theory of infinite sets.
Many of the claims of absolutism in its various forms follow from its identification with rigid
logical structure introduced for these epistemological purposes. Thus according to absolutism
mathematical knowledge is timeless, although we may discover new theories and truths to
add; it is superhuman and ahistorical, for the history of mathematics is irrelevant to the nature
and justification of mathematical knowledge; it is pure isolated knowledge, which happens to
be useful because of its universal validity; it is value-free and culture-free, for the same
reason.
There is a growing body of opinion that the absolutist philosophies of mathematics constitute
a cul de sac, being based on the false hope of providing absolute and eternally incorrigible
foundations for mathematical knowledge. Due to a range of profound philosophical and
technical problems, including Gödel’s incompleteness theorems, such foundations have not,
and most would say, cannot be provided (Davis and Hersh 1980, Ernest 1991, Kitcher 1983,
Lakatos 1976, Tiles 1991, Tymoczko 1986). However, the ensuring "loss of certainty" (Kline
1980) for mathematics does not represent a loss of knowledge. Just as in modern physics
where general relativity and quantum uncertainty indicate the boundaries of current
epistemology, so too the fallibilistic bounds of mathematical knowing represent an increase in
meta-knowledge. Mathematical proofs remain the most certain warrants for knowledge in the
possession of humanity. But we need to acknowledge that proofs vary in strength as
knowledge warrants and not reify them into something timeless and absolute.
Fallibilist Philosophies of Mathematics
In the past few decades a new wave of philosophies of mathematics have been gaining
ground, and these propose a non-absolutist account of mathematics. Kitcher and Aspray
(1988) described this as the ‘maverick’ tradition that emphasises the practice of, and human
side of mathematics, and characterises mathematical knowledge as historical, changing and
corrigible. This position has been termed quasi-empiricist and fallibilist, and is associated
with constructivist and post-modernist thought in education (Glasersfeld 1995), philosophy
(Rorty 1979), and the social sciences (Restivo 1992). A growing number of modern
3
philosophers of mathematics and mathematicians espouse fallibilist views of mathematics
(see Ernest 1994 and above references).
One of the innovations associated with a fallibilist view of mathematics is a reconceptualised
view of the nature of mathematics. It is no longer seen as defined by a body of pure and
abstract knowledge which exists in a superhuman, objective realm (the World 3 of Popper
1979). For accuracy the false image of perfection of mathematics must be dropped (Davis
1972).
Fallibilism views mathematics as the outcome of social processes. Mathematical knowledge
is understood to be fallible and eternally open to revision, both in terms of its proofs and its
concepts. Consequently this view embraces as legitimate philosophical concerns the practices
of mathematicians, its history and applications, the place of mathematics in human culture,
including issues of values and education - in short - it fully admits the human face and basis
of mathematics. The fallibilist view does not reject the role of structure or proof in
mathematics. Rather it rejects the notion that there is a unique, fixed and permanently
enduring hierarchical structure (Davis and Hersh 1980, Ernest 1991, Lakatos 1976,
Tymoczko 1986).
2. Values of Mathematics
Philosophical treatments of values are distributed among several branches of philosophy
including ethics (moral values such as the good), aesthetics (values such as beauty), political
philosophy (political values such as right action), and educational philosophy (educational
values and goals). However, epistemology and the philosophy of mathematics and science are
not usually included in this list. Thus the relationship between values and mathematics (or
science) is a controversial issue. Traditional epistemologies and absolutist philosophies of
mathematics deny that values have any place or relevance with respect to mathematical
knowledge. In contrast fallibilism asserts that mathematics is human and hence imbued with
human values.
This controversy can be partly sidestepped because it is uncontroversial to assert that
education in general, and mathematics (or science) education in particular, are value laden.
Thus even the subject called school mathematics (or science) can uncontroversially be
asserted to be value-laden because there are decisions made as to how it is selected, shaped,
represented and communicated in schools, that are based on preferences and what is valued.
There are many treatments of values in education and mathematics education. In general
education the seminal treatment is that of Krathwohl, et al. (1964), although this characterises
value-systems rather than the specific values held by individuals and groups. In mathematics
education a number of authors have treated values including Bishop (1988), Mellin-Olsen
(1988), Skovsmose (1994) and Ernest (1991, 1995). Bishop (1999) provides the most explicit
treatment and review of the field. He distinguishes three levels of the values of individuals.
1. Ideological, towards mathematics.
2. Individual, towards themselves, e.g., as learners of mathematics
3. Social, towards society in relation to mathematics education.
4
In this section I shall focus on two ideological values, as attributed to the discipline of
mathematics (subsequently looking at values that might be described as individual or social).
Because of its character as a science there are a number of values identified with
mathematics. These include respect for truth (Wilson 1986), precision, definiteness, economy
of representation (symbolization), beauty and power.
However, for my main point I will draw on two sets of contrasting values not usually applied
to mathematics, based on Gilligan’s (1982) theory of values. Gilligan distinguishes
‘separated’ and ‘connected’ values positions. The ‘separated’ position valorises rules,
abstraction, objectification, impersonality, unfeelingness, dispassionate reason and analysis,
and tends to be atomistic and thing- or object-centred in focus. The ‘connected’ position is
based on and valorises relationships, connections, empathy, caring, feelings and intuition, and
tends to holistic and human-centred in its concerns. It has been called an ‘ethic of care’
(Larrabee 1993).
Gilligan did not have mathematics or science in mind when she distinguished these two value
positions. Rather she was trying to characterise stereotypically masculine (separated) and
feminine values (connected) of the West. However, ignoring its gendered or feminist source I
wish to use this theory because of the loose parallel with the absolutism and fallibilism in the
philosophy of mathematics, and authoritarian and humanistic images of mathematics,
respectively.
Before I dismiss the gender dimension, let me make it clear that I believe that both men and
women have both a masculine and feminine side3, but the separated values that are
stereotypically masculine in the West have come to dominate many of the institutions and
structures in modern society, including mathematics and science. Purely separated values
focus on instrumental, technical and utilitarian or profit-driven activities and perspectives and
discount the cooperative, human and caring side of life. My argument is not that we need to
abandon the separated values and worldview. This is a central and valuable pillar of human
thought and being, especially in mathematics and science. But separated values need to be
balanced (not replaced) by connected values in mathematics, school, business, government
and society, for the benefit and inclusion of all. 4
Distinguishing between two contrasting sets of values for mathematics there is:
1. Separated values emphasizing rules, abstraction, objectification, impersonality,
dispassionate reason, analysis, atomism and object-centredness. These are values that
are associated with a view of mathematics as a product, a body of knowledge with the
role of humans minimized or factored out.
2. Connected values emphasizing relationships, connections, processes, empathy, caring,
feelings and intuition, holism and human-centredness. These values foreground the
role of human activity in mathematics.
3
Note that reviews of empirical evidence do not support any easy dichotomisation of male and female values,
even considering the West alone. Bradbeck (1983) reviews published studies and argues that differences in
values and ethical views are much greater within than across the two sexes.
4
I have discussed these values and their relationship with mathematics more fully in Ernest (1991, 1995).
5
3. Images of Mathematics
Before discussing the relationship of images of mathematics with values and epistemology it
is necessary to indicate what I mean by an image of mathematics in this context. I will take an
image of mathematics to be a representation of mathematics that is either social or personal.
Social images of mathematics are public representations encompassing mass media
representations including films, cartoons, pictures, popular music, etc; presentations and
displays in school mathematics classrooms and the learning experiences in them; parent, peer
or other narratives about mathematics; representations of mathematics utilising any other
semiotic education modes or means; etc.
Personal images of mathematics are personal representations of mathematics utilising some
form of mental picture, visual, verbal, narrative or other personal representation, originating
from past experiences of mathematics, or from social talk or other representations of
mathematics, potentially comprising cognitive affective and behavioural dimensions. The
conception of mathematics as it is represented in such images may vary across a range
encompassing research mathematics and mathematicians, school mathematics, and
mathematical applications everyday or otherwise.
Social and personal images of mathematics are intimately related, as personal images result
from exposure to social images of mathematics including mathematics learning experiences
in the classroom. Social images of mathematics are constructed by individuals or groups
based on their own personal images, represented and made public. However, both kinds of
image may have implicit elements which individuals are unaware of or which are portrayed
publicly without conscious deliberation.
Negative and separated images of mathematics
A widespread public image of mathematics in the West is that it is difficult, cold, abstract,
theoretical, ultra-rational, but important and largely masculine. It also has the image of being
remote and inaccessible to all but a few super-intelligent beings with ‘mathematical minds’
(Buerk 1982, Buxton 1981, Ernest 1996, Lim and Ernest 1998, Picker and Berry 2000).
Many persons operating at high levels of competency in numeracy, graphicacy, computeracy
in their professional life in the UK still say "I’m no good at mathematics, I never could do it."
In contrast to the shame associated with illiteracy, innumeracy has been almost a matter of
pride amongst educated persons in western Anglophone countries. In fact, many such persons
are not innumerate at all, and it is school or academic mathematics not everyday mathematics
that they feel they cannot do. Numeracy, contextual mathematics, even ethnomathematics are
widely perceived to be quite distinct from school/academic mathematics, and the latter is
understood to be ‘real’ mathematics.
For many people this negative image of mathematics is also associated with anxiety and
failure. When Brigid Sewell was gathering data on adult numeracy for the Cockcroft (1982)
Inquiry she asked a sample of adults on the street if they would answer some questions. Half
of them refused to answer further questions when they understood it was about mathematics,
suggesting negative attitudes. Extremely negative attitudes such as ‘mathephobia’ (Maxwell
1989) probably only occur in a small minority in western societies, and may not be significant
6
at all in other countries. Nevertheless it is an important phenomenon, and I have never heard
of an equivalent ‘literaphobia’, although literacy is at least as important as numeracy.
The negative popular image of mathematics sets it apart from daily concerns of the public,
despite the many social applications of mathematics referred to daily in the mass-media, from
sports and weather to economic and social indicators. Thus the widespread public image of
mathematics is largely a negative and remote one, alien to many persons’ professional and
personal concerns and their self-perceived abilities.
Let me now summarise the negative public image of mathematics. Mathematics is perceived
to be rigid, fixed, logical, absolute, inhuman, cold, objective, pure, abstract, remote and ultrarational. This description closely resembles the separated values listed above. For this reason
I shall also call it a separated image of mathematics.
By identifying what is perceived to be a negative image of mathematics with separated values
there is the danger of slipping in a gratuitous value judgement. For there is a strong
consonance between separated values and absolutist philosophies of mathematics. But an
absolutist image of mathematics can exist without the negative connotations I have described.
For the absolutist image of mathematics is precisely what attracts some persons to it. Many
mathematicians love mathematics just for its absolutist features. It is both consistent and
common for teachers and mathematicians to hold an absolutist and separated view of
mathematics as neutral and value free, but to regard mathematics teaching as necessitating the
adoption of humanistic, connected values. In my research on student teacher’s attitudes and
beliefs about mathematics I found a subgroup of mathematics specialists who combined
absolutist conceptions of the subject with very positive attitudes to mathematics and its
teaching (Ernest 1988, 1989b). So to call their image of mathematics negative would be
inappropriate and incorrect.
Nevertheless, for simplicity, I shall argue that when a philosophy of mathematics is used as
the basis for an image of mathematics and is combined with separated values, the outcome is
a separated image of mathematics, and that this is frequently if not universally associated with
negative attitudes to mathematics.
Positive images of mathematics
Positive images of mathematics associate a wholly different set of characteristics with the
subject. One widespread positive image is that mathematics is a dynamic, problem-driven and
continually expanding field of human creation and invention (Lim and Ernest 1999). This
view places most emphasis on mathematical activity, the doing of mathematics, and it accepts
that there are many ways of solving any problem in mathematics. It views mathematics as
approachable and accessible, human and personal, practical, concerned with processes of
inquiry and understanding and creative and flexible uses of knowledge to solve problems.
Part of the approachability of mathematics is that anyone should be able to solve problems
and check answers, and that problems have multiple solution methods and multiple answers.
This makes it accessible to all, and is the humanistic image promoted by progressive
mathematics education.
Another more extreme positive image of mathematics is that it is artistic, beautiful,
emotional, exciting, full of joy and wonder, awesome, inspiring, fascinating, entrancing,
delightful, absorbing, and life enhancing. Such a view is not very common among the general
7
public, although some elements of it are reported (Lim and Ernest 1999) but it is more often
found among working mathematicians (Burton 2000).
One heartening finding is that the humanistic image, as promoted by progressive mathematics
education reforms, is typically the adjunct of positive attitudes to mathematics (Thompson
1984, Ernest 1988). The positive image of mathematics with its human-centred overtones
emphasizing relationships, connections, feelings and intuition, human activities has many
shared features with the connected values position. For this reason I shall call it a connected
image of mathematics.
A separated image of mathematics in classroom
A separated image of mathematics may be encouraged in school by giving students mainly
unrelated routine mathematical tasks which involve the application of learnt procedures, and
by stressing that every task has a unique, fixed and objectively right answer, coupled with
disapproval and criticism of any failure to achieve this answer. This may not be what the
mathematician recognises as mathematics, but a result is nevertheless an separated conception
of the subject, and is often accompanied by negative attitudes to mathematics.
There is no need for school mathematics to communicate the negative image of mathematics
described above. In fact the world-wide consensus of mathematics educators is that school
mathematics must counter that image, and offer instead something that is personally
engaging, and evidently useful or motivating in some other way, if it is to fulfil its social
functions (NCTM 1989, Howson and Wilson 1986, Skovsmose 1994).
8
4. The interaction of Epistemology and Values and the Resulting Images of
Mathematics
Drawing together the separate parts in the above account the point I want to make is that there
is a parallel between the absolutist philosophy of mathematics, separated values and the
separated image of mathematics. Likewise, a second parallel exists between the fallibilist
philosophy of mathematics, connected values and the connected humanistic image of
mathematics. These parallels are shown by the vertical arrows in Figure 1 connecting the top
three layers.
Figure 1: Simplified Relations between Epistemologies of Mathematics, Values and Images of
Mathematics in School
Absolutist Philosophy
of Mathematics

Separated Values




Fallibilist Philosophy
of Mathematics


Connected Values


(‘crossing
over’)
Separated Image of
School Mathematics



Connected Image of
School Mathematics



Constraints and Opportunities afforded by Social Context


Separated Image of
Mathematics Realised
in Classroom

 
(‘strategic
compliance’
or ‘hidden
curriculum’)



Connected Image of
Mathematics Realised
in Classroom


Filtered via student interpretations, attitudes and beliefs


Separated Image of
Mathematics held by
Learner
 
(‘preconceptions’)


Connected Image of
Mathematics held by
Learner
However, Fig. 1 also illustrates another possibility, that of ‘crossing over’. This shows how
an absolutist philosophy of mathematics if combined with connected values can give rise to a
connected image of school mathematics. A deep commitment to the ideals of progressive
mathematics education can and frequently does co-exist with a belief in the objectivity and
neutrality of mathematics, especially amongst mathematics teachers and educators.
Fallibilism has no monopoly on this. In cases like these, connected values are often associated
with education and the conception of school mathematics, rather than with academic
(mathematicians’) mathematics. This is illustrated in the figure by the thin black arrows.
9
Contrariwise, it possible for a fallibilist philosophy of mathematics to combine with separated
values, resulting in a separated image of mathematics. An epistemological fallibilist who also
subscribes to separated values might argue that although mathematical knowledge is a
contingent and fallible social construction, so long as it remains accepted by the mathematical
community it is fixed and should be transmitted to learners in this way, and that questions of
school mathematics are uniquely decidable as right or wrong with reference to its
conventional corpus of knowledge. These are attributes of a separated image of mathematics.
Figure 1 also distinguishes images of mathematics at three levels
1. Image of school mathematics: how mathematics is represented within the planned
school curriculum.
2. Image of mathematics realised in the classroom: mathematics as it is actually presented
to students,
3. Image of mathematics held by the learner: the personal image developed or acquired as
a result of classroom (or other) experiences.
This utilizes a three way analysis of the curriculum that distinguishes the planned, taught and
the learned curriculum (Robitaille and Garden 1989).
Fig. 1 illustrates that between a planned and a realized or implemented image of mathematics,
whether separated or connected, lie the constraints and opportunities afforded by the social
context. Turning plans into reality is subject to a variety of barriers, difficulties and obstacles,
and requires utilization of the available resources, possibilities and opportunities (Ernest
1989a).
One of the lessons we have learned from constructivism is that the development of learner
knowledge, attitudes and beliefs are idiosyncratic and to some extent unpredictable as a result
of the complex personal processes of learning (Glasersfeld 1995). There is a consensus that
there can be no mechanical process of transmission of knowledge or image of mathematics to
learners.
Thus Fig. 1 illustrates how the realized image of mathematics as represented/manifested in
the classroom is filtered via student interpretation, perception, sense-making through existing
conceptions, attitudes and beliefs before contributing to the formation and elaboration of
learners’ personal images of mathematics.
Because of the discontinuities between the three types of image of mathematics, new
opportunities are admitted for shifts in image of mathematics. Fig. 1 illustrates how a teacher
with connected values and a connected (planned) image of school mathematics might
nevertheless forced into ‘strategic compliance’ (Lacey 1977) with the imposed school
sanctioned pedagogy, so that the image of mathematics realised in classroom is a separated
one. This could be a temporary consequence of contextual constraints, but if permanent might
lead to tension and stress for the teacher. This state of affairs is indicated in the Fig. 1 by the
bold and thin arrows deviating left towards a separated classroom image under the impact of
the social context. These arrows may originate with either an absolutist philosophy (thin
arrows), or a fallibilist philosophy (bold arrows), but in both cases cross over, resulting in a
separated realised image of mathematics in the classroom. Empirical research has confirmed
that teachers with very distinct personal philosophies of mathematics (absolutist and
10
fallibilist) have been constrained by the social context of schooling to teach in a traditional,
separated way (Lerman 1986).
Although not so widely reported, the opposite shift of strategic compliance is also
conceivable, whereby a teacher with separated values and separated (planned) image of
mathematics is forced to strategically comply by the constraints of the social context to
provide a connected image of mathematics in the classroom. The likelihood of such an
outcome is diminished by the difficulties of realizing a connected image of mathematics
without teacher behaviours such as encouraging open-ended exploratory work, which is
difficult to accomplish without belief and commitment.
Similarly, although they are subjected to an enacted or realized image of mathematics that is
largely connected, because of the import of student preconceptions in their interpretations of
their experience they might pick up on what they perceive to be indicators of a separated
image of mathematics in the classroom. This is shown in Fig. 1 as the impact of preconceptions, with leftward deviating arrows. The opposite directional influence is also
theoretically possible. That is, students because of their preconceptions might personally
reinterpret or ‘misconstrue’ the image of mathematics realized in the classroom and maintain
their own oppositely characterised image of mathematics.
There is a further dimension I should bring into the account, which has not yet been explicitly
mentioned. This is the contrast between the overt and the hidden curriculum. At all three
levels of the curriculum it is possible to identify hidden or unintended values and images of
mathematics that are not part of the planned education system. The intended curriculum often
includes unplanned, implicit and hidden values that may subvert the planned values. The
implemented curriculum very often contains unplanned values enacted by the teacher and
classroom representations that may contradicted the teacher espoused classroom values and
image of mathematics. Lastly the ‘acquired’ or learner constructed values and image of
mathematics, as evidenced in learner behaviours, may not be what was intended to be
attained. So the process of transmission of epistemologies and values into image of
mathematics realized in the classroom and in learner images is not fully controllable and
predictable, as a variety of unplanned forces and contingencies may help to shape or distort
the final outcomes.
Conclusion
I have argued that epistemologies and values play a vital role in the production of classroom
images of mathematics. There is a substantial literature linking personal philosophies of
mathematics and belief systems with classroom mathematics. For example, Thom (1973:
204) asserts that “All mathematical pedagogy, even if scarcely coherent, rests on a philosophy
of mathematics.” Empirical research (e.g., Cooney 1988) has confirmed claims that “teachers'
views, beliefs and preferences about mathematics do influence their instructional practice”
(Thompson 1984: 125).
What I have suggested here is that values play a decisive role in linking epistemologies and
philosophies of mathematics with what happens in the classroom, and in particular, with the
image of mathematics planned for, realized and acquired in the mathematics classroom. In
summary my thesis is that epistemology plus values equals – in the sense of gives rise to –
11
classroom image of mathematics. Thus my claim is that values play a vital part in the
mathematics classroom, one that is under-recognized. It should be noted that this general
thesis can be asserted independently of the specific philosophies of mathematics and sets of
values (separated or connected) in the above analysis.
Of course, like any analysis made in terms of dichotomies, the above account is simplified,
perhaps even simplistic. Human beings do not fall neatly into two boxes. In my earlier
analysis of mathematics curriculum ideologies (Ernest 1991) I suggested five basic
ideological types and distinguished over a dozen components for each ideology, and even that
model was a simplification. Nevertheless, such simplified models can suggest the way that
important theoretical factors impact on the teaching and learning of mathematics and suggest
ways forward in terms of both research and practice (Ernest and Greenland 1990).
Finally, it might be asked why images of mathematics, and particularly learners’ images of
mathematics matter. Why should one be concerned about the images of mathematics
communicated to learners? The answer is that images of mathematics make up in large part of
learners’ attitudes and beliefs about mathematics. These play an important part in individual
and societal success. Attitudes and beliefs concerning mathematics play an important role in
facilitating problem solving performance and capabilities (Lester et al. 1994, Schoenfeld
1992). Secondly, attitudes and beliefs about mathematics are important factors in determining
learner participation and enrolment in further related studies and career choices. It is widely
acknowledged, the study of mathematics is important both for learner life-chances and for
society (Ernest 1995). Thus developing positive image of mathematics in learners is
important both for social advancement and for individual learner benefits. Furthermore,
parallel arguments, both in terms of individual and societal importance, and concerning the
positive impact of images via attitudes and beliefs, can be made in the areas of science and
technology.
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